© Electronic Publishing House COMMON FIXED POINT THEOREMS FOR SEMIGROUPS ON METRIC SPACES

Abstract. This paper consists of two main results. The first one shows that if S is a left reversible semigroup of selfmaps on a complete metric space (M,d) such that there is a gauge function ϕ for which d(f(x),f (y)) ≤ϕ(δ(Of (x,y))) for f ∈ S and x,y in M, where δ(Of (x,y)) denotes the diameter of the orbit of x,y under f, then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M, the sequence of iterates {fn(x)} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M,d)